1. For lines lm,, and p, l m and m p. Which of the following statement(s) is/are possible? I. l intersects p III. l p A. 6 B. 5 C. 3.5 D. 2.

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1 NOA means Nne f hese Answers are crrect, and shuld be chsen when chices A, B, C and D are nt crrect. Diagrams may nt be drawn t scale. means parallel. means perpendicular. 1. Fr lines lm,, and p, l m and m p. Which f the fllwing statement(s) is/are pssible? I. l intersects p II. l p III. l p IV. l and p are skew Gemetry pic est FAMA State Cnventin A straight weed stands upright in a lake s that 8 inches f it are expsed abve the water. A fisherman pulls the tp f the weed tward shre, and the weed stays straight as it is pulled, and the length f the weed remains unchanged. he tp disappears when it is 10 inches hrizntally frm the riginal place where it std upright. Hw deep is the lake, in inches, where the weed riginally std upright? A. B. 5 C..5 D A. II nly B. I, III nly C. I, III, IV nly D. I, II, III nly V W x y 20 y 5 Q SU is parallel t V, and they intersect transversal Q at pints and W respectively. S, and U are cllinear; V, W and are cllinear. m S 2x (2 x), S U m W ( x y 20) and m QW (y 5). Give the value f 2y x. A. 15 B. 20 C. 25 D ints, Q, and S are n the circle as shwn. mqs 170 and m Q 50. m Q 5. Give m. A. 90 B. 85 C. 80 D E 5. ight H triangle EFG is shwn with FH altitude t hyptenuse F G EG, EH < HG. H is between E and G. FH= and EG=15. Give the length f EF. A. B. C. 5 D S

2 . 8 A regular square pyramid has base edge 8. It is truncated (chpped ff) by a plane parallel t its riginal square 8x8 base. his truncatin created a square tp base f edges each, and the tp base is a distance f frm the bttm base. ell the vlume f the riginal pyramid. A. 148 B. 512 C. 21 D. 25 Gemetry pic est FAMA State Cnventin A (a+20) E 110 4a 9. entagn ENA has interir angles that measure 80, 110, (a+20), a, and (4a), in degrees. Give the degree measure f the largest angle f ENA. A. 170 B. 15 C D. 140 a N 7. An arc in a circle f radius 12 cm has length L cm. ell the area in sq. cm f the sectr bunded by the same arc and the central angle that intercepts the arc, in terms f the numerical cnstant L. A. L B. L C. L D. 1.5L 8. he area f a regular hexagn is 25. Give the perimeter f the hexagn. A. 12 B. 10 C. 9 D A gat is fenced in a rectangular field, 20 m by 12 m. he gat is tied t the middle f ne f the 20 m lng fences by a rpe 2 m lng. here is a gap that the gat can squeeze thrugh in the exact midpint f the ther 20 m lng fence (assume a pint). he number f square meters f land that the gat can graze n is p q, fr p 0. Give the value f p q. (Disregard any dimensins f the gat in cmputatins, and assume graze-able land where the gat can reach.) A. 00 B C. 01 D. 02

3 Gemetry pic est FAMA State Cnventin 2017 p q S 11. Lines p and q are parallel and 4 units apart. and S are n line q. S=5. Hw many distinct pints n line p can be used as the third vertex t make S issceles? A. 8 B. C. 5 D angent segment S has pint f tangency. Secant segment SU U cntains chrd U. If U is units frm the center f the circle, and its length is twice that f S and the circle s radius is 5, give the length f S. A. 4 2 B. 4 C. 2 D. 1. A square piece f paper is flded in half vertically, s that the crease is parallel t ne side. If the resultant shape has perimeter 24 cm, what is the area f the riginal square, in sq. cm? A. 4 B. 2 C. 2 D. 2 2 S 14. he wner f #10 s gat built him a brand new rectangular pen! he length is 1 feet and the height is 5 ft. If the gat is secured 4 ft frm ne crner n ne f the lng sides with a 10 ft rpe, then the number f square feet the gat cannt reach n the p q inside f his pen is. Give the value f p q. Disregard the dimensins f the gat. If the end f the rpe des nt reach, then assume he cannt reach the grund there. A. 400 B. 85 C. 220 D X S W 9 V U 8 Y 12 Cnsider rectangle SU abve, with pints W, Y, and X n the sides as shwn. XV S, XV=, S=9, W=, UY=8 and Y=12. Give the perimeter f pentagn XVYW. A. 4 B. C. 8 D. 40 G

4 Gemetry pic est FAMA State Cnventin A circle with equatin 2 2 x y 10x 2y 74 0 has a tangent line at pint ( 1,7). he equatin f this tangent line is y mx b. Give the value f 12( m b). A. 104 B. 102 C. 100 D A triangle has sides with lengths 5, 8 and 10. Which describes the triangle? A. right B. acute C. btuse D. skew 18. A right square pyramid has lateral edges f length 10 each, and a height f 4. Give the vlume f the pyramid. 21. V S U A cable is strung frm at the tp f ne ple t a pint n the grund, which is directly between S and U, and then t the tp f a secnd ple at V. he ples are perpendicular t the grund, have negligible radii, and S VU. S=10, UV=5 and SU=8. Find the ttal length f the cable (+V). A. 1 B C. 1 D. 17 A. 5 B. 400 C. 72 D A cnvex plygn has ttal interir angle sum f 210 degrees. If the plygn has n sides, give the sum f the digits f n. A. 5 B. 4 C. D A cnvex slid has 120 edges and 0 faces. Hw many vertices des it have? A. 92 B. 94 C. 9 D Q U V S Q, U and S are pints f tangency f the sides f V t the inscribed circle shwn. U 1.5( U ) 4( QV ) and the perimeter f V is 40. What is the length f the shrtest side f V? A. 80 B. 100 C. 110 D. 120

5 Q S U 2. he circle abve has center Q.,, U, and are n circle Q. Diameter is extended t S. Q. If Q= and S=1 then give the length f SU, with U the pint where S meets circle Q. Gemetry pic est FAMA State Cnventin egular entagn SUV is inscribed in a circle. If p units is the perimeter f SUV and q square units is the area f SUV, then the rati 2 p q ktan m, fr integers k and m and 0 m 90. Give the sum k m. A. 84 B. 7 C. 4 D. 5 is A. 2 B C. D Q 24. SV has side lengths S=8, 10 V=10 8 and SV=12. is the bisectr S U V f SV and U is the median t side SV. If and U are between S and V, then find the length U. A. 1 B. 2 C. 1 D. 2 S has pints Q and S n sides as shwn. QS. If the area f QS is 7 then give the area f quadrilateral QS. A. 280 B C. 49 D he medians drawn frm the acute angles f a right triangle have lengths 5 and 12 respectively. he length f the p hyptenuse f the triangle is q fr psitive integer p, and psitive prime q. Give the value f p q. A. 1 B. 0 C. 28 D. 1

6 Gemetry pic est FAMA State Cnventin A triangle has sides f lengths 1, 14 and 15. Hw many f the altitudes f the triangle have integer lengths? A. 0 B. 1 C. 2 D. 29. A mnkey swings n a 120 ft vine that is anchred t a limb f a tree at a pint. 0. A square is circumscribed abut a circle. A regular hexagn is inscribed in the same circle. ell the rati f the perimeters f the square and the hexagn. A. 4 B. 4 C. 2 D. he first swing cntains an angle f 100 degrees. Each subsequent angle is 4 the degree measure f his previus swing. hat is, he swings right fr 100 degrees, then left fr 75 degrees, etc. Give the ttal distance he swings, in feet. A B. C D. 100